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On the period of sequences (An(p)) in intuitionistic propositional calculus

Published online by Cambridge University Press:  12 March 2014

Wim Ruitenburg
Wim Ruitenburg*
Affiliation:
New Mexico State University, Las Cruces, New Mexico 88003
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Abstract

In classical prepositional calculus for each proposition A(p) the following holds: ⊢A(p) ↔ A3(p). In this paper we consider what remains of this in the intuitionistic case. It turns out that for each proposition A(p) the following holds: there is an n ∈ N such that

As a byproduct of the proof we give some theorems which may be useful elsewhere in propositional calculus.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 3 , September 1984 , pp. 892 - 899
Copyright
Copyright © Association for Symbolic Logic 1984

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References

REFERENCES

[1]Nishimura, I., On formulas in one variable in intuitionistic propositional calculus, this Journal, vol. 25 (1960), pp. 327–331.Google Scholar
[2]Smoryński, C., Applications of the Kripke models, in [3, pp. 324–391].Google Scholar
[3]Troelstra, A. S. (editor), Metamathematical investigation of intuitionistic arithmetic and analysis, Lecture Notes in Mathematics, vol. 344, Springer-Verlag, Berlin, 1973.CrossRefGoogle Scholar